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# M03-24

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:20
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55% (hard)

Question Stats:

52% (00:46) correct 48% (00:38) wrong based on 239 sessions

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If $$n$$ is a positive integer, is $$n^x$$ an even number?

(1) $$n$$ is an even number

(2) $$x^2-3x+2 = 0$$

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:21
Official Solution:

If $$n$$ is a positive integer, is $$n^x$$ an even number?

(1) $$n$$ is an even number. If $$x=0$$ then $$n^x=1=\text{odd}$$ but if $$x=1$$ then $$n^x=n=\text{even}$$. Not sufficient.

(2) $$x^2-3x+2 = 0$$. Either $$x=1$$ or $$x=2$$. Not sufficient, since no info about $$n$$.

(1)+(2) Since given that $$n=\text{even}$$ then both $$n^1$$ and $$n^2$$ will be even. Sufficient.

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Manager
Joined: 10 May 2014
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20 Dec 2014, 17:32
2
This question shows how important it is to sometimes restate the question in our own words before diving into the statements (not too far away from the Prethinking in Critical Reasoning, huh?)

Question Stem "Prethinking"
For the expression to be an even number, we need 2 things:
I) n must be an even number
II) x must be integer and positive.

Statement 2: Factor the quadratic and you´ll get (x - 1)(x - 2) = 0. Therefore, x = 1 or x = 2. This addresses II but doesn´t address I --> Not Sufficient
(1) + (2): both conditions are addressed --> Sufficient.
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Joined: 21 May 2015
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02 Jun 2015, 05:41
C
(1) is suff for any value of x except 0 when the results become 1
(2) lets us see that x is not 0 but insuff as n is not known

thus both are suff together
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Apoorv

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02 Jun 2015, 11:24
But N is a positive integer. Does that mean zero can be positive?
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03 Jun 2015, 03:22
meshackb wrote:
But N is a positive integer. Does that mean zero can be positive?

0 is neither positive nor negative. Where are we considering n = 0 in the solution above?
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03 Jun 2015, 03:36
For n^x to be even
1-> n has to be even number
2--> x needs to b a positive integer.

Statement 1 gives us the first condition but does not tell about the value of.
Statement 2 gives us x=1 or 2 which gives us the second conditions but does not tell us about the value of n.

So by combining both statements we have both required conditions fulfilled.

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Current Student
Joined: 14 Oct 2013
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04 Jun 2015, 16:43
This question sparked something for me.. can fractions be considered even or odd? For example in statement 1 what if x were negative? So lets say n=4 and x=-2. I assume we don't consider 1/16 to be even since when divided by 2 it does not produce an integer?

Thanks!
Math Expert
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05 Jun 2015, 04:51
healthjunkie wrote:
This question sparked something for me.. can fractions be considered even or odd? For example in statement 1 what if x were negative? So lets say n=4 and x=-2. I assume we don't consider 1/16 to be even since when divided by 2 it does not produce an integer?

Thanks!

1. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder. Even integers are: ..., -6, -4, -2, 0, 2, 4, 6, 8, ...

2. An odd number is an integer that is not evenly divisible by 2: ..., -5, -3, -1, 1, 3, 5, ...

Theory on Number Properties: math-number-theory-88376.html
Tips on Number Properties: number-properties-tips-and-hints-174996.html

All DS Number Properties Problems to practice: search.php?search_id=tag&tag_id=38
All PS Number Properties Problems to practice: search.php?search_id=tag&tag_id=59

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05 Dec 2015, 02:31
even stronger for (1) is that x must not be an integer as there is no info about x in (1) .. so n^x is not even necessarily integer
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31 Aug 2017, 21:53
Take away:
Making inferences from the DS question is very critical.

If we understand that the n cannot be odd and x has to more then 0, then this question can become very simple.

S1 merely tells us that n is even. Without knowing the value of x we can have multiple value of n which can be odd or even.
S2 gives us the information about the value of x, which after factorization can be 1 and 2. But without any information about n we cannot know if n to the power x is even.

S1+S2 give us the complete information about the question. They tell us that n is even and x is either 1 or 2 that means we will certainly have an even no for the question. After all, that’s what we inferred from the question stem.

Thank you.
Please press kudos if this question has helped you in anyway.
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25 May 2018, 15:35
It is given that (in the question stem) n is a positive integer, that means n>0
Now, if S1 specifies that, n is also even, that means n>1
Thus, eg: 2^x where x irrespective of being odd or even is still going to leave n^x as even

On solving S2 we get S as either 1 or 2. Thus, insufficient

And, I arrived at answer as A

Kindly let me know how do I guard against such ambiguity, of what is specified in the question stem vs the Statements. I mean should I consider statements independent of the question stems or Should question stems stand as true come what may.

Thanks, Pls correct me if I am wrong.
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26 May 2018, 00:29
nshivapu wrote:
If $$n$$ is a positive integer, is $$n^x$$ an even number?

(1) $$n$$ is an even number. If $$x=0$$ then $$n^x=1=\text{odd}$$ but if $$x=1$$ then $$n^x=n=\text{even}$$. Not sufficient.

(2) $$x^2-3x+2 = 0$$. Either $$x=1$$ or $$x=2$$. Not sufficient, since no info about $$n$$.

(1)+(2) Since given that $$n=\text{even}$$ then both $$n^1$$ and $$n^2$$ will be even. Sufficient.

It is given that (in the question stem) n is a positive integer, that means n>0
Now, if S1 specifies that, n is also even, that means n>1
Thus, eg: 2^x where x irrespective of being odd or even is still going to leave n^x as even

On solving S2 we get S as either 1 or 2. Thus, insufficient

And, I arrived at answer as A

Kindly let me know how do I guard against such ambiguity, of what is specified in the question stem vs the Statements. I mean should I consider statements independent of the question stems or Should question stems stand as true come what may.

Thanks, Pls correct me if I am wrong.

On the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other or the stem.
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In this question notice that the stem says that n is a positive integer and then (1) says that it's even, so n could be 2, 4, 6, 8, ... Notice also, that neither the stem nor the first statement says anything about x. It could be even or odd, it could be a fraction, or an irrational number.

If x is a positive integer, then n^x = (positive even integer)^(positive integer) = even. But if say x is a fraction, then n^x won't necessarily be even, for example, if n = 2 and x = 1/2, then $$n^x=\sqrt{2}$$, which is not an integer, hence is not even. Or consider example given in the solution: $$x=0$$ then $$n^x=1=\text{odd}$$. So, from (1) n^x could be even, odd or not an integer at all, which means that (1) is NOT sufficient.

Does this make sense?
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Re: M03-24   [#permalink] 26 May 2018, 00:29
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# M03-24

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